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In a Shirt factory, there are three processes named A,B, and C.They manufactures 25%, 35%, 40% of production respectively.of these 5%, 4%, 2% are defective.What is the probability the randomly selected shirt is of the defective one produced by process C?Options 1669 2869 2769

Question

In a Shirt factory, there are three processes named A,B, and C.They manufactures 25%, 35%, 40% of production respectively.of these 5%, 4%, 2% are defective.What is the probability the randomly selected shirt is of the defective one produced by process C?Options 1669 2869 2769

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Solution

To solve this problem, we need to use the concept of conditional probability.

Step 1: Identify the given probabilities.

  • Probability of a shirt being manufactured by process A, P(A) = 25% = 0.25

  • Probability of a shirt being manufactured by process B, P(B) = 35% = 0.35

  • Probability of a shirt being manufactured by process C, P(C) = 40% = 0.40

  • Probability of a shirt being defective given it was manufactured by process A, P(D|A) = 5% = 0.05

  • Probability of a shirt being defective given it was manufactured by process B, P(D|B) = 4% = 0.04

  • Probability of a shirt being defective given it was manufactured by process C, P(D|C) = 2% = 0.02

Step 2: Calculate the total probability of a shirt being defective.

P(D) = P(A) * P(D|A) + P(B) * P(D|B) + P(C) * P(D|C) = 0.25 * 0.05 + 0.35 * 0.04 + 0.40 * 0.02 = 0.0125 + 0.014 + 0.008 = 0.0345

Step 3: Calculate the probability that a randomly selected defective shirt is produced by process C.

We use the formula for conditional probability: P(C|D) = P(D|C) * P(C) / P(D)

P(C|D) = 0.02 * 0.40 / 0.0345 = 0.008 / 0.0345 = 0.2318840579710145

So, the probability that a randomly selected defective shirt is produced by process C is approximately 0.232 or 23.2%.

None of the given options match this result.

This problem has been solved

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